Math CentralQuandaries & Queries


Question from Sampson, a student:

I'm looking to set up a weekly schedule within a 22 week segment of 2 7 team divisions where every team plays every other team in their divison 3 times and have 4 cross over games with 4 of the other 7 teams in the other division. I've yet to figure this out.
Thanks for your time.


It takes seven weeks for 7 teams to play each other once because some team has a bye each week. To get a 22-week schedule, you can do this:

Suppose the teams in each division are numbered 1, 2, ..., 7.

It is easy to make a schedue for a group of 7 teams to play each other once each. There is an example in the archives: Use it three times for each division to get the in-division games.

The first time through, make sure that teams with the same number have a bye in the same week, so that 1 plays 1, 2 plays 2, ..., 7 plays 7.

After 7 weeks you will have one round of in-division games, and one round of between division games completed.

The next time through, rearrange the schedule to make sure that the bye teams in the 7 weeks are such that 1 plays 2, 2 plays 3, ..., 7 plays 1. The next time, do it so that 1 plays 3, 2 plays 4, ..., 6 plays 1, 7 plays 2.

In week 22 there will be 7 crossover games: 1 plays 4, 2 plays 4, ..., 5 plays 1, 6 plays 2, 7 plays 3.


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